This paper proposes a new load torque observer based on the Takagi-Sugeno fuzzy method for a permanent magnet synchronous motor(PMSM). A Linear Matrix Inequality(LMI) parameterization of the fuzzy observer gain is given, and the LMI conditions are derived for the existence of the fuzzy load torque observer guaranteeing $alpha$-stability and linear quadratic performance. In this paper, a nonlinear speed controller is employed to validate the performance of the proposed fuzzy load torque observer, and various simulation results are presented under motor parameter and load torque variations.